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mechanical engineering

Questions and Answers of Mechanical Engineering

Two identical 0.9-lb slender rods AB and BC are welded together to form an L-shaped assembly. The assembly is guided by two small wheels that roll freely in inclined parallel slots cut in a vertical
For the truck of Sample Prob. 16.1, determine the distance through which the truck will skid if(a) The rear-wheel brakes fail to operate,(b) The front-wheel brakes fail to operate.
Knowing that the coefficient of static friction between the tires and the road is 0.80 for the automobile shown, determine the maximum possible acceleration on a level road, assuming (a) Four-wheel
The support bracket shown is used to transport a cylindrical can from one elevation to another. Knowing that μs = 0.30 between the can and the bracket, determine? (a) The magnitude of the upward
Solve Prob. 16.7 assuming that the acceleration a of the bracket is downward.
A 50-lb cabinet is mounted on casters that allow it to move freely (μ = 0) on the floor. If a 25-lb force is applied as shown, determine (a) The acceleration of the cabinet, (b) The range of values
Solve Prob. 16.9 assuming that the casters are locked and slide on thorough floor (μs = 0.25).
Bars AB and BE, each of weight 8 lb, are welded together and are pin-connected to two links AC and BD. Knowing that the assembly is released from rest in the position shown and neglecting the masses
Members ACE and DCB are each 30 in. long and are connected by a pin at C. The mass center of the 20-lb member AB is located at G. Determine (a) The acceleration of AB immediately after the system has
A 4-kg uniform slender rod AB is held in position by two ropes and the link CA which has a negligible weight. After rope BD is cut the assembly rotates in a vertical plane under the combined effect
A 4-kg uniform slender rod AB is held in position by two ropes and the link CA which has a negligible weight. After rope BD is cut the assembly rotates in a vertical plane under the combined effect
The 7.5-kg rod BC connects a disk centered at A to crank CD. Knowing that the disk is made to rotate at the constant speed of 180 rpm, determine for the position shown the vertical components of the
At the instant shown the tensions in the vertical ropes AB and DE are 300N and 200N, respectively. Knowing that the mass of the uniform bar BE is 5kg, determine, at this instant, (a) The force P, (b)
Draw the shear and bending-moment diagrams for each of the bars AB and BE of Prob. 16.11.
Draw the shear and bending-moment diagrams for the connecting rod BC of Prob. 16.15.
For a rigid slab in translation, show that the system of the effective forces consists of vectors ors (Δmi)a attached to the various particles of the slab, where a is the acceleration of the mass
For a rigid slab in centroidal rotation, show that the system of the effective forces consists of vectors ?? (Δmi) ω2r'i and (Δmi) (α × r'i) attached to the various particles Pi of the slab,
A 200-kg flywheel is at rest when a constant 300 N ??? m couple M is applied at time t = 0. At t = 28s the flywheel reaches its rated speed of 2400 rpm and the couple is removed. Knowing that the
A 500-lb flywheel is at rest when a constant 200 lb ?? ft couple M is applied at time t = 0. At t = 30 s the flywheel reaches its rated speed of 3000 rpm and the couple is removed. Assuming that the
The flywheel shown consists of a 30-in.-diameter disk which weighs 240 lb. The coefficient of friction between the band and the flywheel is 0.35. If the initial angular velocity of the flywheel is
The 100-mm-radius brake drum is attached to a flywheel which is not shown. The drum and flywheel together have a mass of 300 kg and a radius of gyration of 600 mm. The coefficient of kinetic friction
A 10-kg uniform disk is placed in contact with an inclined surface and a constant 11 N ?? m couple M is applied as shown. The weight of the link AB is negligible. Knowing that the coefficient of
A 10-kg uniform disk is placed in contact with an inclined surface and a constant couple M is applied as shown. The weight of the uniform link AB is 5 kg and the coefficient of kinetic friction at D
Each of the double pulleys shown has a mass moment of inertia of 20 kg ?? m2 and is initially at rest. The outside radius is 400 mm, and the inner radius is 200 mm. Determine (a) The angular
The flywheel shown has a radius of 600 mm, a mass of 144 kg, and a radius of gyration of 450 mm. An 18-kg block A is attached to a wire that is wrapped around the flywheel, and the system is released
In order to determine the mass moment of inertia of a flywheel of radius 1.5 ft, a 20-lb block is attached to a wire that is wrapped around the flywheel. The block is released and is observed to fall
Two disks A and B, of mass mA = 2kg and mB = 4kg, are connected by a belt as shown. Assuming no slipping between the belt and the disks, determine the angular acceleration of each disk if a 2.70N ??
The 25-lb double pulley shown is at rest and in equilibrium when a constant 3.5 lb ??ft couple M is applied. Neglecting the effect of friction and knowing that the radius of gyration of the double
The weight and radius of friction disk A are WA = 12 lb and rA = 6 in.; the weight and radius of friction disk B are WB = 6 lb and rB = 4 in. The disks are at rest when a couple M of moment 7.5 lb ??
Solve Prob. 16.32 assuming that the couple M is applied to disk B.
Two identical 16-lb uniform cylinders are at rest when a constant couple M of magnitude 3 ft ??lb is applied to cylinder A. Knowing that the coefficient of kinetic friction between cylinder B and the
Two identical 16-lb uniform cylinders are at rest when a constant couple M of magnitude 3 ft ??lb is applied to cylinder A. Knowing that the coefficient of kinetic friction between the cylinders is
A cylinder of radius r and mass m rests on two small casters A and B as shown. Initially, the cylinder is at rest and is set in motion by rotating caster B clockwise at high speed so that slipping
In Prob. 16.36 assume that no slipping can occur between caster B and the cylinder (such a case would exist if the cylinder and caster had gear teeth along their rims). Derive an expression for the
Disk B has an angular velocity ω0 when it is brought into contact with disk A, which is at rest. Show that (a) The final angular velocities of the disks are independent of the coefficient of
The 12-lb disk A has a radius us rA = 6 in. and an initial angular velocity ω0 = 750 rpm clockwise. The 30-lb disk B has a radius rB = 10 in. and is at rest. A force P of magnitude 5 lb is then
Solve Prob. 16.39 assuming that disk A is initially at rest and that disk B has an angular velocity of 750 rpm clockwise.
Show that the system of the effective forces for a rigid slab in plane motion reduces to a single vector, and express the distance from the mass center G of the slab to the line of action of this
For a rigid slab in plane motion, show that the system of the effective forces consists of vectors ors (Δmi)a, ??(Δmi)ω2ri, and (Δmi), (α × ri) attached to the various particles Pi of the slab,
A force P of magnitude 0.75 lb is applied to a tape wrapped around a thin 6-lb hoop. Knowing that the hoop rests on a frictionless horizontal surface, determine the acceleration of (a) Point A, (b)
A force P is applied to a tape wrapped around a uniform disk that rests on a frictionless horizontal surface. Show that for each 360? rotation of the disk the center of the disk will move a distance
A uniform slender rod AB rests on a frictionless horizontal surface, and a force P of magnitude 2 N is applied at A in a direction perpendicular to the rod. Knowing that the rod has a mass of 3 kg,
A 120-kg satellite has a radius of gyration of 600 mm with respect to the y axis and is symmetrical with respect to the zx plane. Its orientation is changed by firing four small rockets A, B, C, and
The steel roll shown weighs 2800 lb, has a centroidal radius of gyration of 6 in., and is lifted by two cables looped around its shaft. Knowing that for each cable TA = 690 lb and TB = 730 lb,
Immediately after the force P is applied to the plate of Prob. 16.47, determine the acceleration of (a) Point A, (b) Point B.
A uniform slender L-shaped bar ABC is at rest on a horizontal surface when a force P of magnitude 4 N is applied at point A. Neglecting friction between the bar and the surface and knowing that the
The steel roll shown weighs 2800 lb, has a centroidal radius of gyration of 6 in., and is lifted by two cables looped around its shaft. Knowing that for each cable TA = 690 lb and TB = 730 lb,
The steel roll shown weighs 2800 lb, has a centroidal radius of gyration of 6 in, and is lifted by two cables looped around its shaft. Knowing that at the instant shown the acceleration of the roll
A drum of 200-mm radius is attached to a disk of radius rA = 150 mm. The disk and drum have a combined mass of 5 kg and a combined radius of gyration of 120 mm and are suspended by two cords. Knowing
A drum of 200-mm radius is attached to a disk of radius rA = 140 mm. The disk and drum have a combined mass of 5 kg and are suspended by two cords. Knowing that the acceleration of point B on the
The uniform disk shown, of mass m and radius r, rotates counterclockwise. Its center C is constrained to move in a slot cut in the vertical member AB and a horizontal force P is applied at B to
The 12-lb uniform disk shown, of radius r = 3.2 in, rotates counterclockwise. Its center C is constrained to move in a slot cut in the vertical member AB and a 11-lb horizontal force P is applied at
A uniform slender L-shaped bar ABC is at rest in a vertical plane when two upward forces are applied as shown. Knowing that the mass of the bar is 20 kg, determine (a) The initial angular
A uniform slender L-shaped bar ABC is at rest in a vertical plane when two upward forces are applied as shown. Knowing that the mass of the bar is 20 kg, determine (a) The initial angular
A beam AB of mass m and of uniform cross section is suspended from two springs as shown. If spring 2 breaks, determine at that instant (a) The angular acceleration of the beam, (b) The acceleration
A beam AB of mass m and of uniform cross section is suspended from two springs as shown. If spring 2 breaks, determine at that instant (a) The angular acceleration of the beam, (b) The acceleration
A uniform slender bar AB of mass m is suspended from two springs as shown. If spring 2 breaks, determine at that instant (a) The angular acceleration of the bar, (b) The acceleration of point A, (c)
A thin plate of the shape indicated and of mass m is suspended from two springs as shown. If spring 2 breaks, determine the acceleration at that instant (a) Of point A, (b) Of point B. A square plate
A thin plate of the shape indicated and of mass m is suspended from two springs as shown. If spring 2 breaks, determine the acceleration at that instant (a) Of point A, (b) Of point B. A thin hoop of
A thin plate of the shape indicated and of mass m is suspended from two springs as shown. If spring 2 breaks, determine the acceleration at that instant (a) Of point A, (b) Of point B. A circular
A sphere of radius r and mass m is projected along a rough horizontal surface with the initial velocities indicated. If the final velocity of the sphere is to be zero, express, in terms s of v0, r,
A bowler projects a 200-mm-diameter ball of mass 5 kg along an alley with a forward velocity v0 of 5 m/s and a backspin ω0 of 9 rad/s, knowing that the coefficient of kinetic friction between the
Solve Prob. 16.65 assuming that the bowler projects the ball with the same forward velocity but with a backspin of 18 rad/s.
A uniform sphere of radius r and mass m is placed with no initial velocity on a belt that moves to the right with a constant velocity v1. Denoting by μk the coefficient of kinetic friction between
Solve Prob. 16.67, assuming that the sphere is replaced by a wheel of radius r, mass m, and centroidal radius of gyration k.
A sphere of radius r and mass m has a linear velocity v0 directed to the left and no angular velocity as it is placed on a belt moving to the right with a constant placed velocity v1. If after first
Show that the couple I α of Fig. 16.15 can be eliminated by attaching the vectors mat and man at a point P called the center of percussion, located on line OG at a distance GP = k2/r from the mass
A uniform slender rod of length L = 36 in. and weight W = 10 lb hangs freely from a hinge at C. A horizontal force P of magnitude 15 lb is applied at end B. Knowing that r = 9 in., determine (a) The
In Prob. 16.71, determine(a) The distance r for which the horizontal component of the reaction at C is zero,(b) The corresponding angular acceleration of the rod.
A uniform slender rod of length h L = 900 mm and mass m = 1 kg hangs freely from a hinge at A. If a force P of magnitude 3.5 N is applied at B horizontally to the left (h = L), determine (a) The
In Prob. 16.73, determine(a) The distance h for which the horizontal component of the reaction at A is zero,(b) The corresponding angular acceleration of the rod.
A portion of a circular cylindrical shell forms a small vane which is welded to the vertical shaft AB. The vane and shaft rotate about the y axis with a constant angular velocity of 180 rpm
A uniform slender rod AB of length L and mass m is pivoted at end A and released from a horizontal position. The angular velocity of the rod as it passes through the vertical position is known to be
A 120-mm-diameter hole is cut as shown in a thin disk of 600-mm diameter. The disk rotates in a horizontal plane about its geometric center A at the constant rate of 480 rpm. Knowing that the disk
A uniform slender rod of mass 350 g/m is used to form the assembly shown. The assembly rotates clockwise at a constant rate of 120 rpm under the combined effect of gravity and the couple M which
A uniform rod of length L and mass m is supported as shown. If the cable attached at B suddenly breaks, determine (a) The acceleration of end B, (b) The reaction at the pin support.
A uniform rod of length L and mass m is supported as shown. If the cable attached at B suddenly breaks, determine (a) The distance b for which the acceleration of end A is maximum, (b) The
A half cylinder of mass m is released from rest in the position shown and swings freely about the horizontal diameter AB. Determine, at this instant, (a) The acceleration of point D, (b) The
A uniform rod of length L and mass m is supported as shown. Knowing that cable AD suddenly breaks, determine at this instant (a) The angular acceleration of the rod, (b) The tensions in cables AE and
A 4-kg slender rod is welded to the edge of a 3-kg uniform disk as shown. The assembly rotates about A in a vertical plane under the combined effect of gravity and of the vertical force P. Knowing
Two identical 4-lb slender rods AB and BC are connected by a pin at B and by the cord AC. The assembly rotates in a vertical plane under the combined effect of gravity and a 6 lb ?? ft couple M
Two identical 4-lb slender rods AB and BC are connected by a pin at B and by the cord AC. The assembly rotates in a vertical plane under the combined effect of gravity and a couple M applied to rod
Two slender rods, each of length l and mass m, are released from rest in the position shown. Knowing that a small frictionless knob at end B of rod AB bears on rod CD, determine immediately after
Derive the equation ΣMC = IC α for the rolling disk of Fig. 16.17, where ΣMC represents the sum of the moments of the external forces about the instantaneous center C, and IC is the moment of
Show that in the case of an unbalanced disk, the equation derived in Prob. 16.87 is valid only when the mass center G, the geometric center O, and the instantaneous center C happen to lie in a
A flywheel is rigidly attached to a shaft of 30-mm radius that can roll along parallel rails as shown. When released from rest, the system rolls 5 m in 40 s. Determine the centroidal radius of
A flywheel of centroidal radius of gyration k is rigidly attached to a shaft that can roll along parallel rails. Denoting by μs the coefficient of static friction between the shaft and the rails,
A homogeneous sphere S, a uniform cylinder C, and a thin pipe P are in contact when they are released from rest on the incline shown. Knowing that all three objects roll without slipping, determine,
An 80-lb uniform cylinder is acted upon by a 50-lb force as shown. Knowing that the cylinder rolls without slipping, determine (a) The acceleration of its center G, (b) The minimum value of the
A drum of 4-in. radius is attached to a disk of 8-in. radius. The disk and drum have a total weight of 10 lb and combined radius of gyration of 6 in. A cord is attached as shown and pulled with a
A drum of 4-in. radius is attached to a disk of 8-in. radius. The disk and drum have a total weight of 10 lb and combined radius of gyration of 6 in. A cord is attached as shown and pulled with a
A drum of 4-in. radius is attached to a disk of 8-in. radius. The disk and drum have a total weight of 10 lb and combined radius of gyration of 6 in. A cord is attached as shown and pulled with a
A drum of 4-in. radius is attached to a disk of 8-in. radius. The disk and drum have a total weight of 10 lb and combined radius of gyration of 6 in. A cord is attached as shown and pulled with a
A drum of 80-mm radius is attached to a disk of 160-mm radius. The disk and drum have a combined mass of 5 kg and combined radius of gyration of 120 mm. A cord is attached as shown and pulled with a
A drum of 80-mm radius is attached to a disk of 160-mm radius. The disk and drum have a combined mass of 5 kg and combined radius of gyration of 120 mm. A cord is attached as shown and pulled with a
A drum of 80-mm radius is attached to a disk of 160-mm radius. The disk and drum have a combined mass of 5 kg and combined radius of gyration of 120 mm. A cord is attached as shown and pulled with a
A drum of 80-mm radius is attached to a disk of 160-mm radius. The disk and drum have a combined mass of 5 kg and combined radius of gyration of 120 mm. A cord is attached as shown and pulled with a
A 10-lb uniform square plate is supported by two identical 3-lb uniform slender rods AD and BE. It is held in the position shown by rope CF. Determine, immediately after rope CF has been cut, (a) The
Solve Prob. 16.101 assuming that rod AD is replaced by a cable of negligible mass.
Gear C has a mass of 5 kg and a centroidal radius of gyration of 75 mm. The uniform bar AB has a mass of 3 kg and gear D is stationary. If the system is released from rest in the position shown,

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